Insurances on a Status (Several Lives)

Abstract

We consider several lives x, y,..., z with future lifetimes X, Y,..., Z resp. A status on the lives x, y,..., z is a fictitious life ρ, such that the event ρ↑t (:⇔ ρ is alive at t), depending on X, Y,..., Z, is defined for all t≥0. Then the event ρ↓t (:⇔ ρ is dead at t) is the negation of event ρ↑t:

$$\rho \downarrow t: \Leftrightarrow not\left( {\rho \uparrow t} \right) \Leftrightarrow :\left( {\rho \uparrow t} \right),$$

where the notation of App.B (Multiple events) is used. Hence, the status ρ can equally well be defined by the events ρ↓t (t≥O) as by the events ρ↑t (t≥0).